UDK 519.7
DEPENDENCE OF THE REGRESSION ESTIMATOR PROPERTIES OF A PROBABILITY DENSITY ON SINGULARITIES OF ITS SYNTHESIS TECHNIQUE
D. V. Borisov [1], A. V. Lapko [1], [2], V. A. Lapko [1], [2]
[1]Siberian State Aerospace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation Е-mail: valapko@yandex.ru [2]Institute of Computational Modeling, Siberian Branch of RAS 50, Akademgorodok, Krasnoyarsk, 660036, Russian Federation Е-mail: lapko@icm.krasn.ru
Approximating properties of the regression estimator of a probability density are investigated. Estimation synthesis is based on decomposition of initial statistical data and the analysis of probabilistic characteristics of received sets of random variables. Dependence of the regression estimator properties of a probability density on methods of digitization of an interval of values of a random variable is established. A deviation mean square procedure of an optimum choice of an amount of intervals of digitization is defined from a condition of a minimum of asymptotic expression. The received formula depends on an aspect of a restored probability density and volume of a priori data. Outcomes of researches are important to the solution of the problems of a hypothesis test about distributions of random variables and a confidential estimation of a probability density.
probability density, regression estimator, approximating properties, digitization methods.
References
  1. Lapko A. V., Lapko V. A. Avtometriya. 2002, no. 5, p. 38–48.
  2. Lapko V. A., Kapustin A. N. Avtometriya. 2006, vol. 42, no. 6, p. 26–33.
  3. Lapko A. V., Lapko V. A. Avtometriya. 2008, vol. 44, no. 3, p. 65–74.
  4. Lapko A. V., Lapko V. A., Egorochkin I. A. Sistemy upravlenija i informacionnye tehnologii. 2009, no. 1 (35), p. 60–64.
  5.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2009, no. 3.1 (37), p. 156–160.
  6. 6. Lapko A. V., Lapko V. A. Avtometriya. 2010, vol. 46, no. 1, p. 70–78.
  7.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2010, no. 1 (39), p. 16–19.
  8.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2010, no. 1.2 (39), p. 300–304.
  9.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2010, no. 3 (41), p. 8–11.
  10.  Lapko A. V., Lapko V. A. Avtometriya. 2010, vol. 46, no. 6, p. 47–53.
  11.  Lapko A. V., Lapko V. A. Avtometriya. 2011, vol. 47, no. 4, p. 76–82.
  12. Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologiju. 2011, no. 1 (43), p. 12–15.
  13.  Lapko A. V., Lapko V. A. Informatika i sistemy upravlenija. 2013, no. 1 (35), p. 119–126.
  14.  Lapko A. V., Lapko V. A. Avtometriya. 2003, vol. 39, no. 1, p. 54–61.
  15.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2012, no. 3 (49), p. 152–156.
  16.  Epanechnikov V. A. Teorija verojatnosti i ee primenenija. 1969, vol. 14, no. 1, p. 156–161.
  17.  Lapko A. V., Lapko V. A. Izmeritel'naja tehnika. 2013, no. 7, p. 24–27.
  18.  Lapko A. V., Lapko V. A. Optimal selection of the number of sampling intervals in domain of variation of a one-dimensional random variable in estimation of the probability density (2013) Measurement Techniques, 56 (7), p. 24–27. doi: 10.1007/s11018-013-0279-x. 

Borisov Dmitry Vladimirovich – Student, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: dimbo2007@yandex.ru

Lapko Alexander Vasilyevich – Doctor of Engineering Science, professor, Leading researcher of Institute of Computational Modelling of Russian Academy of Sciences, Siberian Branch, professor of the Space craft and Technologies Department, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: lapko@icm.krasn.ru

Lapko Vasily AlexandrovichDoctor of Engineering Sciences, associate professor, Leading researcher of Institute of Computational Modelling of the Russian Academy of Sciences, Siberian Branch, head of the Space craft and Technologies Department, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: valapko@yandex.ru